# Statistics "Mayfield high school" - the taller the person the more they weigh.

Extracts from this document...

Introduction

Raheem Mirza Mathematic Coursework

Candidate No : 2149

MATHS COURSEWORK

STATISTICS

“MAYFIELD HIGH SCHOOL”

STUDENT: RAHEEM MIRZA

TEACHER: MS LEWIS

## Part 1: Introduction/Aim

I imagine that the taller the person is the more they weigh, due to body mass. I also assume that the gender doesn’t have an effect on their height and weight. I will try and prove or disprove this in my investigation. I will take people from Key Stage 3.

Part 2: Method:

## Using Microsoft Excel, i selected 40 random people from the Mayfield High School database. I chose to use the formula =SUM ()*40. This automatically gave me 40 students which are below.

## Part 3: My 40 Random Result

Random Result | Number | Year Group | Gender | Height (cm) | Weight (kg) |

671 | 1 | 9 | Female | 159 | 50 |

687 | 2 | 9 | Female | 156 | 50 |

261 | 3 | 7 | Male | 156 | 39 |

342 | 4 | 8 | Female | 175 | 64 |

584 | 5 | 9 | Female | 180 | 82 |

445 | 6 | 8 | Male | 167 | 51 |

388 | 7 | 8 | Female | 180 | 58 |

428 | 8 | 8 | Male | 154 | 37 |

646 | 9 | 9 | Female | 165 | 52 |

291 | 10 | 8 | Female | 168 | 59 |

224 | 11 | 7 | Male | 148 | 26 |

309 | 12 | 8 | Female | 163 | 42 |

654 | 13 | 9 | Female | 165 | 49 |

469 | 14 | 8 | Male | 165 | 40 |

262 | 15 | 7 | Male | 149 | 35 |

353 | 16 | 8 | Female | 160 | 46 |

635 | 17 | 9 | Female | 160 | 40 |

804 | 18 | 9 | Male | 180 | 42 |

685 | 19 | 9 | Female | 152 | 50 |

388 | 20 | 8 | Female | 180 | 58 |

479 | 21 | 8 | Male | 168 | 51 |

75 | 22 | 7 | Female | 166 | 45 |

94 | 23 | 7 | Female | 173 | 51 |

552 | 24 | 9 | Female | 160 | 60 |

548 | 25 | 8 | Male | 152 | 45 |

468 | 26 | 8 | Male | 182 | 54 |

238 | 27 | 7 | Male | 160 | 40 |

630 | 28 | 9 | Female | 162 | 41 |

750 | 29 | 9 | Male | 180 | 55 |

258 | 30 | 7 | Male | 157 | 48 |

271 | 31 | 7 | Male | 151 | 39 |

560 | 32 | 9 | Female | 152 | 46 |

739 | 33 | 9 | Male | 160 | 68 |

792 | 34 | 9 | Male | 170 | 50 |

416 | 35 | 8 | Male | 148 | 40 |

684 | 36 | 9 | Female | 158 | 55 |

335 | 37 | 8 | Female | 175 | 55 |

430 | 38 | 8 | Male | 162 | 53 |

176 | 39 | 7 | Male | 152 | 32 |

470 | 40 | 8 | Male | 165 | 59 |

Types of Formulae

I will use the following types of formulae;

- Quartile Ranges
- Mean, Mode, Median and Range
- Pearson’s Product Moment Correlation Co-Efficient

To represent my data, I intend to use the following types of Graphs;

- Cumulative Frequency Graphs
- Histograms
- Frequency Polygons
- Box and Whisker Plots

Part 5:

I will now work out the mean, mode, range and median of the data. I have decided to use intervals because height and weight are continuous data.

Frequency table for height of boy’s and girls

Height Interval | Tally | Frequency (f) | Midpoint (x) | f (x) |

148 – 154 | 9 | 151 | 1359 | |

155 – 161 | 10 | 158 | 1580 | |

162 – 168 | 11 | 135 | 1485 | |

169 – 175 | 4 | 172 | 688 | |

176 – 182 | 6 | 179 | 1074 | |

Total: | ∑f=40 | ∑x=795 | ∑fx=6188 |

Mean: 6188/40 = 154.7

Mode Interval: 162 – 168

Median: 162 – 168

Range: 182 – 148 =34

Frequency table for weights of boy’s and girls

Weight Interval | Tally | Frequency (f) | Midpoint (x) | f (x) |

26 –32 | 2 | 29 | 58 | |

33 – 39 | 4 | 36 | 144 | |

40 – 46 | 11 | 43 | 473 | |

47 – 53 | 11 | 50 | 550 | |

54 – 60 | 8 | 57 | 456 | |

61 – 67 | 2 | 64 | 128 | |

68 – 74 | 1 | 71 | 71 | |

75 – 81 | 0 | 78 | 0 | |

82 – 88 | 1 | 85 | 85 | |

Total: | ∑f=40 | ∑x=513 | ∑fx=1965 |

Mean: 1965/40 =49.13 2dp

Modal Interval: 40 – 46 and 47 – 53

Median: 47 – 53

Range: 82 – 26 =56

## Part 6: PMCC for my 40 students

Random Result | Number | Height (y) (cm) | Weight (x) (kg) | xy |

671 | 1 | 159 | 50 | 7950 |

687 | 2 | 156 | 50 | 7800 |

261 | 3 | 156 | 39 | 6084 |

342 | 4 | 175 | 64 | 11200 |

584 | 5 | 180 | 82 | 10440 |

445 | 6 | 167 | 51 | 5698 |

388 | 7 | 180 | 58 | 8580 |

428 | 8 | 154 | 37 | 9912 |

646 | 9 | 165 | 52 | 3848 |

291 | 10 | 168 | 59 | 6846 |

224 | 11 | 148 | 26 | 8085 |

309 | 12 | 163 | 42 | 6600 |

654 | 13 | 165 | 49 | 5215 |

469 | 14 | 165 | 40 | 7300 |

262 | 15 | 149 | 35 | 6400 |

353 | 16 | 160 | 46 | 7560 |

635 | 17 | 160 | 40 | 7600 |

804 | 18 | 180 | 42 | 10440 |

685 | 19 | 152 | 50 | 8568 |

388 | 20 | 180 | 58 | 7470 |

479 | 21 | 168 | 51 | 8823 |

75 | 22 | 166 | 45 | 7470 |

94 | 23 | 173 | 51 | 8823 |

552 | 24 | 160 | 60 | 9600 |

548 | 25 | 152 | 45 | 6840 |

468 | 26 | 182 | 54 | 11648 |

238 | 27 | 160 | 40 | 6400 |

630 | 28 | 162 | 41 | 6642 |

750 | 29 | 180 | 55 | 9900 |

258 | 30 | 157 | 48 | 7536 |

271 | 31 | 151 | 39 | 5889 |

560 | 32 | 152 | 46 | 6992 |

739 | 33 | 160 | 68 | 10880 |

792 | 34 | 170 | 50 | 8500 |

416 | 35 | 148 | 40 | 5920 |

684 | 36 | 158 | 55 | 8690 |

335 | 37 | 175 | 55 | 9625 |

430 | 38 | 162 | 53 | 8586 |

176 | 39 | 152 | 32 | 4864 |

470 | 40 | 165 | 59 | 9735 |

n=40 | ∑y=1930 | ∑x=6527 | ∑xy=318312 |

∑x² =1068757 ∑y² =96454

Formulae for PMCC

The information for the following formulae is above, where the PMCC for the students is worked out.

Middle

Tally

Frequency (f)

Midpoint (x)

F (x)

152 – 158

4

155

620

159 – 165

8

162

1296

166 – 172

2

169

338

173 – 179

3

176

528

180 - 186

3

183

549

Total:

∑f=20

∑x=845

∑fx=3331

Mean: 3331/20 = 166.55

Mode: 159 – 165

Median: 159 – 165

Range: 180-152 =28

Group frequency table for the height of boy’s

Height | Tally | Frequency (f) | Midpoint (x) | F (x) |

148 – 154 | 7 | 151 | 1057 | |

155 – 161 | 4 | 158 | 632 | |

162 – 168 | 5 | 165 | 825 | |

169 – 175 | 1 | 172 | 172 | |

176 – 182 | 3 | 179 | 537 | |

Total: | ∑f=20 | ∑x=825 | ∑fx=3223 |

Mean: 3223/20 = 161.15

Mode: 148 – 154

Median: 155 – 161

Range: 182 – 148 =34

Group frequency table for weight of girl’s

Weight (kg) | Tally | Frequency (f) | Midpoint (x) | F (x) |

40 – 46 | 6 | 43 | 258 | |

47 – 53 | 6 | 50 | 300 | |

54 – 60 | 6 | 57 | 342 | |

61 – 67 | 1 | 64 | 64 | |

68 – 74 | 0 | 71 | 0 | |

75 – 81 | 0 | 78 | 0 | |

82 - 88 | 1 | 85 | 85 | |

Total: | ∑f=20 | ∑x=448 | ∑fx=1049 |

Mean: 1049/20 =52045

Mode: 40 – 46, 47 – 53 and 54 – 60

Median: 47 – 53

Range: 82 –40 =42

Group frequency table for weight of boy’s

Weight (kg) | Tally | Frequency (f) | Midpoint (x) | F (x) |

26 – 32 | 2 | 29 | 58 | |

33 – 39 | 4 | 36 | 160 | |

40 – 46 | 5 | 43 | 215 | |

47 – 53 | 5 | 50 | 250 | |

54 – 60 | 2 | 57 | 114 | |

61 – 67 | 1 | 64 | 64 | |

68 - 74 | 1 | 71 | 71 | |

Total: | ∑f=20 | ∑x=350 | ∑fx=932 |

Mean: 932/20 = 46.6

Mode: 40 – 46 and 47 – 53

Median: 40 – 46

Range: 68 – 26 =42

### Part 9: PMCC for height and weight for females

Number | Height (y) (cm) | Weight (x) (kg) | xy |

1 | 159 | 50 | 7950 |

2 | 156 | 50 | 7800 |

3 | 175 | 64 | 11200 |

4 | 180 | 82 | 14760 |

5 | 180 | 58 | 10440 |

6 | 165 | 52 | 8580 |

7 | 168 | 59 | 9912 |

8 | 163 | 42 | 6846 |

9 | 165 | 49 | 8085 |

10 | 160 | 46 | 7360 |

11 | 160 | 40 | 6400 |

12 | 152 | 50 | 7600 |

13 | 180 | 58 | 10440 |

14 | 166 | 45 | 7470 |

15 | 173 | 51 | 8823 |

16 | 160 | 60 | 9600 |

17 | 162 | 41 | 6642 |

18 | 152 | 46 | 6992 |

19 | 158 | 55 | 5690 |

20 | 175 | 55 | 9625 |

n=20 | ∑y=1053 | ∑x=3309 | ∑xy=14818 |

∑x²=549011 ∑y²=57187

Sxx =549011 – 3309 ²/20 =1536.95

Syy =57187 – 1053²/20 =1746.55

Sxy =175215 – 3309*1053/20 =996.15

r =996.15/√1746.55*1536.95 =996.15/1638.401667 =0.6

### Part 10: PMCC for male height and weight

Number | Height (y) (cm) | Weight (x) (kg) | xy |

1 | 156 | 39 | 6084 |

2 | 167 | 51 | 8517 |

3 | 154 | 37 | 5698 |

4 | 148 | 26 | 3848 |

5 | 165 | 40 | 6600 |

6 | 149 | 35 | 5215 |

7 | 180 | 42 | 7560 |

8 | 168 | 51 | 8568 |

9 | 152 | 45 | 6840 |

10 | 182 | 64 | 11648 |

11 | 160 | 40 | 6400 |

12 | 180 | 55 | 9900 |

13 | 157 | 48 | 7536 |

14 | 151 | 39 | 5889 |

15 | 160 | 68 | 10880 |

16 | 170 | 50 | 8500 |

17 | 148 | 40 | 5920 |

18 | 162 | 53 | 8586 |

19 | 152 | 32 | 4864 |

20 | 165 | 59 | 9735 |

n =20 | ∑y =3226 | ∑x =914 | ∑xy =4140 |

∑x²=522550 ∑y²=43966

Sxx =522550 – 3226²/20 =2196.2

Syy =43966 – 914²/20 =2196.2

Sxy =148818 – 3226*914/2196.2 =1389.8

r = 1389.8/√2196.2*2196.2 =1389.8/2196.2 =0.6

Part 13:

Now I will find the equation of the line of best fit in all three scatter graphs.

Equation of the line of scatter graph 1 considering the point’s A and B.

All of my samples

A =(65,178)

B =(33.5,150)

Gradient =(y2 – y1)/(x2 - x1)

=178-150/65-33.5

=8/9

y =8/9x + c

Intercept (c) using co-ordinate (65,178)

178 =(8/9*65) + c

178 =(57078) + c

c =120.22 2dp

Equation of line of scatter graph 1

y =8/9x + 120.22

h =8/9w + 120.22

Were h =height and w =weight

Equation of line scatter graph 2 considering point’s A and B

Boys Sample

A =(55,178)

B =(34.5,140)

Gradient =(y2 – y1)/(x2 - x1)

=178 – 140/55 – 34.5

=76/41

y =76/41x + c

Intercept (c) using co-ordinate (55,178)

178 =(76/41*55) + c 2dp

178 – 101.95 + c

c =76.05 2dp

Equation of the line of scatter graph 2

y =76/41x + 76.05

h =76/41w + 76.05

Were h =height and w =weight

Equation of the line of scatter graph 3 considering point’s A and B

Girls Sample

A =(80,180)

B =(40.5,160)

Gradient =(y2 – y1)/(x2 - x1)

=180 – 160/80 – 40.5

=40/79

y =40/79x + c

Intercept (c) using co-ordinate (80,180)

180 =(40/79*80) + c

180 – 40.51 = c

c =139.49 2dp

Equation of the line of scatter graph 3

y =40/79x + 139.49

h =40/79w + 139.49

Were h =height and w =weight

Now I will explain how the equation of the best-fit line can be used. If the weight is known of a student then the height can be estimated using the equation. Also if the height is known the weight can be estimated.

Using my found Formulae(s)

## Example 1

Using the line of scatter graph 3 (girls)

h =40/79w + 139.49

The weight of a female student is 82 kg. The height can be estimated using the equation.

h =(40/79) + 139.49

h =41.51 + 139.49

h =181.01 2dp

## Example 2

The height of a female student is 180 cm. The weight can be estimated using the equation.

h =40/79w + 139.49

180 =40/79w + 139.49

180 – 139.49 =40.51

w =40.51*70/40

w =70.89 2dp

This suggests that if there was a male student with a height of 180 cm then his weight is estimated to be 70.893 3dp

### Part 14: Cumulative Frequency

### Table A

Cumulative frequency table for the height of girls

Height | Frequency | Cumulative Frequency |

152 – 158 | 4 | 4 |

159 – 165 | 8 | 12 |

166 – 172 | 2 | 14 |

173 – 179 | 3 | 17 |

180 - 186 | 3 | 20 |

See Graph 1

## Table B

Cumulative frequency table for the height of boys

Height | Frequency | Cumulative Frequency |

148 – 154 | 7 | 7 |

155 – 161 | 4 | 11 |

162 – 168 | 5 | 16 |

169 – 175 | 1 | 17 |

176 – 182 | 3 | 20 |

See Graph 2

Table C

Cumulative frequency table for the weight of girls

Weight | Frequency | Cumulative Frequency |

40 – 46 | 6 | 6 |

47 – 53 | 6 | 12 |

54 – 60 | 6 | 18 |

61 – 67 | 1 | 19 |

68 – 74 | 0 | 19 |

75 – 81 | 0 | 19 |

82 – 88 | 1 | 20 |

## See Graph 3

## Table D

Cumulative frequency table for the weight of boys

Weight | Frequency | Cumulative Frequency |

26 – 32 | 2 | 2 |

33 – 39 | 4 | 6 |

40 – 46 | 5 | 11 |

47 – 53 | 5 | 16 |

54 – 60 | 2 | 18 |

61 – 67 | 1 | 19 |

68 – 74 | 1 | 20 |

Conclusion

1.52

45

77

11

Female

1.59

42

78

11

Female

1.63

38

79

11

Female

1.62

38

80

11

Female

1.70

60

81

11

Female

1.58

48

82

9

Male

1.60

60

83

9

Male

1.56

60

84

9

Male

1.66

54

85

9

Male

1.66

70

86

9

Male

1.52

52

87

9

Male

1.75

75

88

9

Male

1.65

45

89

9

Male

1.52

54

90

9

Male

1.67

54

91

9

Male

1.71

60

92

9

Male

1.80

48

93

9

Male

1.73

66

94

9

Male

1.55

50

95

9

Male

1.77

66

96

9

Male

1.73

52

97

9

Male

1.54

44

98

9

Male

1.47

42

99

9

Male

1.75

63

100

9

Male

1.62

40

101

9

Male

1.46

45

102

9

Male

1.80

64

103

9

Male

1.50

70

104

9

Male

1.61

38

105

9

Male

1.54

60

106

9

Male

1.55

51

107

7

Male

1.49

47

108

7

Male

1.48

47

109

7

Male

1.63

60

110

7

Male

1.50

40

111

7

Male

1.53

35

112

7

Male

1.54

48

113

7

Male

1.54

51.5

114

7

Male

1.48

26

115

7

Male

1.61

56

116

7

Male

1.65

41

117

7

Male

1.30

35

118

7

Male

1.61

56

119

7

Male

1.47

47

120

7

Male

1.67

60

121

7

Male

1.61

46

122

7

Male

1.50

51

123

7

Male

1.47

45

124

7

Male

1.67

53

125

7

Male

1.50

56

126

7

Male

1.52

45

127

7

Male

1.63

60

128

7

Male

1.43

41

129

7

Male

1.45

31

130

7

Male

1.58

48

131

7

Male

1.60

40

132

7

Male

1.65

35

133

7

Male

1.63

50

134

11

Male

1.94

80

135

11

Male

1.69

65

136

11

Male

1.67

60

137

11

Male

1.5

35

138

11

Male

1.86

80

139

11

Male

1.68

63

140

11

Male

1.68

63

141

11

Male

1.83

75

142

11

Male

1.68

56

143

11

Male

1.65

47

144

11

Male

1.62

92

145

11

Male

1.8

68

146

11

Male

1.68

58

147

11

Male

1.71

54

148

11

Male

1.7

56

149

11

Male

1.62

50

150

11

Male

1.71

57

From the graph we can see there is a strong positive correlation. However to use a statistical way to prove this I will use the Pearson’s Product Moment Correlation Co-Efficient. I have discovered a key in excel which automatically does this calculation without making conscious though.

Below is a guide to use of this control;

This then brings up a screen, I then pressed on ‘Pearson’s’, this automatically brings up the PMCC of the sample.

Product Moment Correlation Co-Efficient of height and weight of boys and girls was calculated to be 0.568279. This means it is a “Moderate Correlation”.

Now I will create a scatter graph of male students which are inclusive in my sample. This can be viewed below;

Similarly, as for this graph from the naked eye the graph seems to be positively correlated. But using Pearson’s Product Moment Correlation Co-Efficient, we will see how much it is correlated, the formulae accessible to us tells us the PMCC between height and weight of boys is 0.639816. This again shows us it is a‘Moderate Correlation’.

Now I will create a scatter graph of female students which are inclusive in my sample. This can be viewed below;

This graph doesn’t really have a correlation to it but using PMCC the correlation is 0.483991. This again is a Moderate correlation.

Extension conclusion

In my initial conclusion, I stated girls were generally heavier than boys. The conclusion which I have come to now is the same as my initial hypothesis. Boys are generally heavier than girls.

- -

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

## Found what you're looking for?

- Start learning 29% faster today
- 150,000+ documents available
- Just £6.99 a month